Chance-Constrained Stochastic Model Predictive Control for Managed Pressure Drilling with Dissolution-Aware Thermodynamic State Augmentation

Abstract

Managed pressure drilling has expanded the feasible operating envelope in wells with narrow pressure margins by enabling active manipulation of surface backpressure and flow-out. However, the same closed-loop actuation that stabilizes bottomhole pressure also complicates diagnosis and mitigation of gas influx events, because pressure and pit-volume signatures become entangled with control actions, compressibility, and temperature-dependent fluid properties. A persistent source of ambiguity is the partitioning of influx gas between dissolved and free phases, which can produce liquid swelling and alter volumetric returns without immediate appearance of a distinct free-gas holdup. This paper develops a risk-aware control architecture that explicitly embeds dissolution-driven swelling into the drilling hydraulics state, enabling proactive mitigation through stochastic model predictive control with chance constraints. The technical contribution is a tractable, differentiable control-oriented model that couples one-dimensional annular mass and momentum balances with a thermodynamic dissolution closure and a bounded, stable discretization suitable for real-time optimization. Uncertainty in fluid properties, frictional pressure losses, sensor bias, and influx parameters is represented through a structured stochastic parametrization. A scenario-based approximation of probabilistic safety constraints is then integrated into a receding-horizon optimizer that selects choke and pump trajectories to minimize operational deviation while keeping bottomhole pressure and surface handling risk within prescribed probabilities. The resulting formulation supports joint inference and control by maintaining consistent uncertainty propagation, and it provides explicit certificates of risk for impending surface gas handling. Numerical experiments demonstrate that dissolution-aware state augmentation reduces spurious conservatism relative to free-gas-only models and improves feasibility in regimes where swelling masks early influx indicators